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Continuous-Time Markov Chains and Applications A Singular Perturbation Approach

This book is concerned with continuous-time Markov chains. It develops an integrated approach to singularly perturbed Markovian systems, and reveals interrelations of stochastic processes and singular perturbations. In recent years, Markovian formulations have been used routinely for nu­ merous real...

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Bibliographic Details
Main Authors: Yin, George G., Zhang, Qing (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1998, 1998
Edition:1st ed. 1998
Series:Stochastic Modelling and Applied Probability
Subjects:
Calculus Of Variations And Optimization
Probability Theory
Mathematical Optimization
Calculus Of Variations
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I Prologue and Preliminaries
  • 1 Introduction and Overview
  • 2 Mathematical Preliminaries
  • 3 Markovian Models
  • II Singularly Perturbed Markov Chains
  • 4 Asymptotic Expansion: Irreducible Generators
  • 5 Asymptotic Normality and Exponential Bounds
  • 6 Asymptotic Expansion: Weak and Strong Interactions
  • 7 Weak and Strong Interactions: Asymptotic Properties and Ramification
  • III Control and Numerical Methods
  • 8 Markov Decision Problems
  • 9 Stochastic Control of Dynamical Systems
  • 10 Numerical Methods for Control and Optimization
  • A Appendix
  • A.1 Properties of Generators
  • A.2 Weak Convergence
  • A.3 Relaxed Control
  • A.4 Viscosity Solutions of HJB Equations
  • A.5 Value Functions and Optimal Controls
  • A.6 Miscellany
  • References

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